Module A Revision
HIGHER
☺
Topic
Understand and use number operations and the relationships
Hierarchy of
between them, including inverse operations (E)
operations
use brackets and BIDMAS (E)
Number
Add, subtract, multiply and divide any number

understand and use positive numbers and negative
integers, both as positions and on a number line (G)

add, subtract, multiply and divide integers (F) and then any
number (E)

multiply or divide any number by powers of 10 (G)

multiply or divide any positive number by a number
between 0 and 1 (E)

multiply and divide by a negative number (E)
Approximate to a specified or appropriate degree of accuracy

use previous understanding of integers and place value to
deal with large positive numbers

round numbers to a given power of 10 (Including round to
the nearest integer) (G)

round to the nearest integer (G), to a given number of
decimal places (F) and to one significant figure (E)
Use calculators effectively and efficiently, including statistical
and trigonometrical functions
 use calculators effectively and efficiently (E)
Ratio

know how to enter complex calculations and use function
keys for reciprocals, squares and powers (D)

enter a range of calculations, including those involving
measures (E)
Use ratio notation

use ratio notation, including reduction to its simplest form;
(E)
know its various links to fraction notation (C/D)
Divide a quantity in a given ratio

divide a quantity in a given ratio (D)

determine the original quantity by knowing the size of one
part of the divided quantity (D)
solve word problems about ratio, including using informal
strategies and the unitary method of solution (D)
Factors, Primes
and multiples
Algebra and
Coordinates
Factors, multiples and primes

use the concepts and vocabulary of factor (divisor),
multiple, common factor, highest common factor, least
common multiple, prime number and prime factor
decomposition (C)
find the product of prime factors (C)
Symbols and notation

distinguish the different roles played by letter symbols in
algebra, using the correct notational conventions for
multiplying or dividing by a given number (F)

know that letter symbols represent definite unknown
numbers in equations(1), defined quantities or variables in
formulae and general, unspecified and independent
numbers in identities(2) (G)
know that in functions, letter symbols define new expressions
or quantities by referring to known quantities(3) (G)
Algebraic terminology

distinguish in meaning between the words ‘equation’,
‘formula’, ‘identity’ and ‘expression’ (G)
Use the conventions for coordinates

use the conventions for coordinates; plot points in all four
quadrants (F)

understand that one coordinate identifies a point on a
number line, two coordinates identify a point in a plane
using the terms ‘1D’ and ‘2D’

use axes and coordinates to specify points in all four
quadrants (F)

locate points with given coordinates(1) (F)
find the coordinates of the midpoint of the line segment AB (E),
given points A and B, then calculate the length AB (C)
Sequences and
formulae
Derive a formula, substitute numbers into a formula and
change the subject of a formula

use formulae from mathematics and other subjects
expressed initially in words (G) and then using letters and
symbols (D-F)
substitute numbers into a formula; derive a formula and
change its subject (C)
Generate terms of a sequence using term-to-term and
position-to-term definitions of the sequence
Linear Equations

generate terms of a sequence using term-to-term and
position-to-term definitions of the sequence (F)

generate common integer sequences (including
sequences of odd or even integers, squared integers,
powers of 2, powers of 10, triangular numbers (F)

use linear expressions to describe the nth term of an linear
sequence, (C/D)
Manipulate algebraic expressions

understand that the transformation of algebraic
expressions obeys and generalises the rules of
generalised arithmetic (E)
manipulate algebraic expressions by collecting like terms (E),
by multiplying a single term over a bracket (E), and by taking
out common factors (D)
Set up and solve simple equations
 set up simple equations (F)

solve simple equations by using inverse operations or by
transforming both sides in the same way (E)

solve linear equations, with integer coefficients, in which
the unknown appears on either side or on both sides of the
equation (D)
solve linear equations that require prior simplification of
brackets, including those that have negative signs occurring
anywhere in the equation, and those with a negative solution
(D)
General measures
Interpret scales and use measurements

interpret scales on a range of measuring instruments,
including those for time and mass (G)

know that measurements using real numbers depend on
the choice of unit

understand angle measure using the associated
language(1) (G)

make sensible estimates of a range of measures in
everyday settings(2) (G)

convert measurements from one unit to another (G)
know rough metric equivalents of pounds, feet, miles, pints
and gallons(3) (F)
Constructions
Draw triangles and other 2D shapes using a ruler and
protractor

measure and draw lines to the nearest millimetre, and
angles to the nearest degree (G)
draw triangles and other 2D shapes using a ruler and
protractor, given information about their side lengths and
angles (E)
Use straight edge and a pair of compasses to do
constructions

use straight edge and a pair of compasses to do standard
constructions, including:
i. an equilateral triangle with a given side (D)
ii.
the midpoint and perpendicular bisector of a line
segment (C)
iii.
the perpendicular from a point to a line, the
perpendicular from a point on a line (C)
the bisector of an angle (C)
Construct loci
find loci, by reasoning, to produce shapes and paths (C/D)
Maps
Trigonometry
Maps, bearings and drawings
 use and interpret maps and scale drawings (E)
use bearings to specify direction and to solve problems (D/E)
Solve 2D problems

Pythagoras
Use Pythagoras’ theorem

Handling Data
understand, recall and use trigonometrical relationships in
right-angled triangles, and use these to solve problems,
including those involving bearings (A)
understand, recall and use Pythagoras’ theorem in 2D,
then 3D problems(1) (C/B)
Experimenting

discuss how data relate to a problem, identify possible
sources of bias and plan to minimise it

identify key questions that can be addressed by statistical
methods

design an experiment or survey and decide what primary
and secondary data to use

design and use data-collection sheets for grouped discrete
and continuous data

gather data from secondary sources, including printed
tables and lists from ICT-based sources

design and use two-way tables for discrete and grouped
data
Processing

draw and produce pie charts for categorical data, and
diagrams for continuous data, frequency diagrams (bar
charts, frequency polygons and fixed interval histograms)
and stem and leaf diagrams (E)

calculate mean, range and median of small data sets with
discrete then continuous data (F/G)

Identify the modal class for grouped data (G)

find the median for large data sets (F) and calculate an
estimate of the mean for large data sets with grouped data
(C/D).

draw and produce cumulative frequency tables and
diagrams, box plots and histograms for grouped
continuous data (B)

find the quartiles and interquartile range for large data sets
(B)
Interpreting

look at data to find patterns and exceptions

interpret a wide range of graphs and diagrams and draw
conclusions (?)

interpret social statistics including index numbers, and
survey data (?)

compare distributions and make inferences, using the
shapes of distributions and measures of average and
range (D/E)

understand that if they repeat an experiment, they may –
and usually will – get different outcomes, and that
increasing sample size generally leads to better population
characteristics (D?)

compare distributions and make inferences, using shapes
of distributions and measures of average and spread,
including median and quartiles (B)
understand and use frequency density (A/B)